Pyramid + tangent - practice problems
Number of problems found: 26
- Sun rays
If the sun's rays are at an angle of 60°, then the famous Great Pyramid of Egypt (which is now 137.3 meters high) has a 79.3 m long shadow. Calculate the current height of the neighboring Chephren pyramid, whose shadow is measured at the same time at 78.8 - Cross-section 62964
The owner must cover the carport with a hipped roof with a rectangular cross-section of 8 m x 5 m. All roof surfaces have the same slope of 30°. Determine the price and weight of the roof if 1 m² cost €270 and weighs 43 kg. - Quadrilateral pyramid
The height of a regular quadrilateral pyramid is 6.5 cm, and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body—round calculations to 1 decimal place. - Tetrahedral pyramid 8
Let all the side edges of the tetrahedral pyramid ABCDV be equally long, and its base let us be a rectangle. Find its volume if you know the deviations A=40° B=70° between the planes of adjacent sidewalls and the base plane. The height of the pyramid is h - Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S. - Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'. - Nine-sided 36071
Calculate the surface area and volume of a regular nine-sided pyramid if the radius of the circle inscribed in the base measures ρ = 12 cm and the height of the pyramid is 24 cm - Base diagonal
In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid. - 4side pyramid
Calculate the volume and surface of the regular four-sided pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees. - Regular quadrangular pyramid
The height of the regular quadrangular pyramid is 6 cm, and the length of the base is 4 cm. What is the angle between the ABV and BCV planes? ABCD is the base, V is the vertex. - Regular quadrangular pyramid
How many square meters are needed to cover the shape of a regular quadrangular pyramid base edge of 10 meters if the deviation lateral edges from the base plane are 68°? Calculate waste 10%. - Tetrahedral pyramid
Calculate the regular tetrahedral pyramid's volume and surface if the area of the base is 20 cm² and the deviation angle of the side edges from the plane of the base is 60 degrees. - Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with a base side of 9 cm and a side wall with the base has an angle of 75°. - Calculate 8354
In a regular pyramid in which the edge of the base is | AB | = 4cm; height = 6cm, calculate the angle of the lines AV and CV, V = vertex. - Quadrilateral pyramid
The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base - Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the base plane is α = 60°. - Angle of two lines
There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV. - Pyramid - angle
Calculate the regular quadrangular pyramid's surface whose base edge measured 6 cm, and the deviation from the plane of the base's sidewall plane is 50 degrees. - Side edges
The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid. - Calculate 36253
Calculate the volume of the pyramid, whose base edge a = 8 cm and the sidewall makes an angle α = 60 ° with the square base.
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